TRANSFORMING LINEAR FUNCTIONS WORKSHEET

Problem 1 : 

Graph f(x) = x and g(x) = x - 5. Then describe the transformation from the graph of f(x) to the graph of g(x).

Problem 2 : 

Graph f(x) = x + 2 and g(x) = 2x + 2. Then describe the transformation from the graph of f(x) to the graph of g (x) .

Problem 3 : 

f(x)  =  x

Problem 4 : 

f(x)  =  -4x - 1

Problem 5 : 

Graph f(x) = x and g(x) = 3x + 1. Then describe the transformations from the graph of f(x) to the graph of g(x).

Problem 6 : 

A trophy company charges $175 for a trophy plus $0.20 per letter for the engraving. The total charge for a trophy with x letters is given by the function f(x) = 0.20x + 175. How will the graph change if the trophy’s cost is lowered to $172? if the charge per letter is raised to $0.50?

Detailed Answer Key

1. Answer : 

The graph of g(x) = x - 5 is the result of translating the graph of f(x) = x, 5 units down.

2. Answer : 

The graph of g(x) = 2x + 2 is the result of rotating the graph of f(x) = x + 2 about (0, 2). The graph of g(x) is steeper than the graph of f(x).

3. Answer : 

To find g(x), multiply the value of m by -1.

In f(x) = x, m = 1.

1(-1)  =  -1   This is the value of m for g(x).

g(x) = -x

4. Answer : 

To find g(x), multiply the value of m by -1.

In f(x) = -4x - 1, m = -4.

-4(-1)  =  4   This is the value of m for g(x).

g(x) = 4x - 1 

5. Answer : 

Find transformations of f(x) = x that will result in g(x) = 3x + 1 :

• Multiply f(x) by 3 to get h(x) = 3x. This rotates the graph about (0, 0) and makes it steeper.

• Then add 1 to h(x) to get g(x) = 3x + 1. This translates the graph 1 unit up.

The transformations are a rotation and a translation.

6. Answer : 

f(x) = 0.20x + 175 is graphed in blue.

If the trophy’s cost is lowered to $172, the new function is g(x) = 0.20x + 172. The original graph will be translated 3 units down. 

If the charge per letter is raised to $0.50, the new function is h(x) = 0.50x + 175. The original graph will be rotated about (0, 175) and become steeper.

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